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17
votes
3answers
331 views

Desktop software with HPC resources for back end number crunching

Our workgroup produces a desktop application that simulates building energy performance. It is a .NET application and when the user is running a lot of simulations, they can be quite time consuming. ...
3
votes
1answer
1k views

Can gsl be compiled with the intel C compiler?

The library itself compiles just fine with icc, but when I try to link to it (using icc for both the driver code and the linker), I get the same error that this question on stackoverflow is asking ...
4
votes
1answer
528 views

PETSc's makefile system can't find MKL

I'm learning PETSc and trying to make the examples written in C. However, when I use the provided makefile, I get the following error: ...
3
votes
1answer
152 views

Introduction for (numerical) linear algebra of random variables

I am in search of an introduction into numerical linear algebra - or, at least, pure linear algebra - that treats the case when the input data are random variables. A typical application would be to ...
7
votes
1answer
5k views

cholesky factorization of block matrices

I have a block matrix (either 2x2 blocks or 3x3 blocks) which is the covariance matrix for a joint space of two or three multivariate normal variables. ie ...
4
votes
3answers
162 views

nuclear reaction fluid modelling

I'm pretty ignorant regarding the dark arts of numerical codes and modelling, but i'm interested in trying to pursue it for a particular pet project. It regards modelling of nuclear reactions like ...
1
vote
1answer
542 views

Stability of forward euler method

I am trying to understand the stability of the forward Euler method. I read there's a model problem to see the stability. $$y'(t) = \lambda y(t) \qquad t \in (0, \infty)$$ $$y(0) = 1$$ then the book ...
2
votes
1answer
55 views

Not Sure How to Solve A System Of Linear Equations In MAPLE13

How can one solve the following system of linear equations in MAPLE 13?I know how to solve a linear equation with one variable floating around but not this one. $$x-2y+3z=10$$ $$3x-2y+z=2$$ $$4x+5y+2z=...
1
vote
1answer
142 views

FEM oscillations for polynomials of degree 1

I have the following eliptic 1-D problem $$-\mu u'' + \beta u' = 1$$ $$u(0) = u'(1) = 1$$ where $\mu = 10e^{-5}$ and $\beta = 1$. For this specific problem I am using the following space steps $h=[0.1,...
4
votes
3answers
542 views

Backward stable projection and normalization of a vector

Given a machine precision unit vector $n$, and an arbitrary vector $v$, I want an unconditionally backward stable method to compute $$f(v) = \frac{v-nn'v}{\left|v-nn'v\right|}$$ In other words, ...
5
votes
2answers
283 views

NVE MD simulation of inert gas: Problem maintaining equilibrium

I have been trying to simulate a simple problem of taking about 100-1000 Ar molecules in a NVE (fixed vol, energy) system with equal speed but randomized velocity, and evolving them to obtain a ...
6
votes
2answers
192 views

Is there a backward stable $\tilde{O}(n \log(1/\epsilon))$ algorithm to factor a complex polynomial?

Finding the roots of a complex polynomial is in general extremely numerically unstable, as discussed in (1). According to Pan ((2), (3)), this produces a cubic complexity lower bound, and he presents ...
4
votes
2answers
2k views

Implementing a finite difference method in Mathematica

I am trying to iterate the following equation $$ x_{k}(n+1)=x_k (n)-\epsilon (x_{k+1}(n)-2x_k(n) +x_{k-1}(n))+\sqrt{\epsilon}\; \eta_{k}(n) $$ where $n$ denotes which time step I'm on and $k$ is the ...
2
votes
1answer
419 views

Customizing Genetic Algorithm on Matlab

The Matlab version is 2012b. I am trying using the built-in GA functionality through the Optimization Tool GUI on Matlab. I want to use bit string chromosome with a given length (for example L=24) and ...
6
votes
1answer
707 views

Wrong Result QR decomposition with Pivoting in LAPACK

I am trying to use LAPACK geqp3 function for QR decomposition with pivoting but result is wrong. I tried almost two days but can't figure out the problem. I compared the result with Matlab and Python ...
2
votes
1answer
44 views

Error in Maple's CellDecomposition Command

I have a simple system that I want to process with the CellDecomposition command of Maple. I don't know why Maple is giving an error here! The code is ...
1
vote
1answer
1k views

software request for solving acoustic wave equation

I am searching some libraries or toolboxes (preferred MATLAB) for solving acoustic wave equation in heterogeneous media with time varying source term, i.e. $$\nabla^2 \psi(\vec{r},t) - \frac{1}{c(\vec{...
2
votes
1answer
869 views

Where can I find Ansys Fluent for ubuntu?

I am new to Ansys Fluent (the Ansys CFD product). Is it a windows-only software? My institute owns copies that work on windows only. Online tutorials on how to install Fluent on ubuntu aren't clear.
3
votes
0answers
335 views

Solving PDE or eigenvalue problems without FEM

Do you know any methods/solvers for PDE or eigenvalue problems like $\begin{cases} \Delta u= 0\ (\text{ or }\lambda u) & \text{ in }\Omega \\ u =0 & \text{ on }\partial \Omega \end{cases}$ (...
0
votes
1answer
536 views

ENO/WENO vs monotone Hermite interpolation

I have see the method PCHIP in matlab that implements the monotone Hermite interpolation method which was originally proposed by Carlson in 1980s. It seem to accomplish the goal of preventing the ...
3
votes
1answer
853 views

Full Multigrid convergence is too slow. What could possibly be causing it?

I've coded full multigrid in Matlab and it doesn't seem to be converging fast enough. When I increase the number of grids or the number of iterations, it converges to the analytical solution. But FMG ...
3
votes
0answers
110 views

exact area resampling [closed]

I do image processing, and right now I need to resample some images taken from slightly different perspectives so I can match up features. The pixel intensities have scientific significance, so I want ...
2
votes
0answers
93 views

System of non-linear ODEs and estimating unspecified initial conditions on Maple 12

I have the following 1st order equations and need to solve them using Maple 12. There are unspecified initial conditions and can only be estimated through the Newton raphson method. My problem is how ...
1
vote
1answer
101 views

classification machinery needed

Consider a set of 7D vectors. Each vector belongs to one of four classes. After mapping to 3D with PCA and coloring each point according its class the dataset looks like as shown below: For the ...
19
votes
2answers
2k views

How to determine if a numerical solution to a PDE is converging to a continuum solution?

The Lax equivalence theorem states that consistency and stability of a numerical scheme for a linear initial value problem is a necessary and sufficient condition for convergence. But for nonlinear ...
16
votes
4answers
5k views

uniform vs. non-uniform grid

It is probably a student level question but I can't exactly make it cleat to myself. Why is it more accurate to use non-uniform grids in the numerical methods? I am thinking in the context of some ...
6
votes
1answer
725 views

how to visualize lattice with periodic, helical, etc. boundary conditions?

I am trying to write a special hexagonal lattice generator, with several kinds of boundary conditions, such as helical BC, periodic BC, and I find it hard to verify whether it works correctly. I tried ...
8
votes
1answer
3k views

What algorithm to use for parallel dense matrix inversion on at most 8 cores?

I need to implement parallel dense matrix inversion for a language I am using that appears to not have an existing library for this (specifically IDL using IDL Bridge for message passing). I am ...
3
votes
1answer
191 views

intuition behind the different discrete norms for Crank Nicolson

I am solving a heat equation $u_t=Au$ with Crank-Nicolson finite-difference method and $A$ is a usual discretization matrix for $u_{xx}$ term. I want to tell something about the whole error vector ...
8
votes
1answer
146 views

Testing and visualizing large index arrays

I will be implementing nodal discontinuous Galerkin method soon, and having done this before I know the basic indexing arrays I will need to compute, given a mesh and polynomial data. The problem I ...
4
votes
3answers
171 views

Numeric solution of simple but possibly singular linear system

I have a simple (and small) linear homogeneous system $Ax=0$, where the entries of the $N\times M$ matrix $A$ are small integers. I do not need fancy methods which efficiently solve almost singular ...
2
votes
1answer
131 views

Extreme points from constraint expression of convex space

I'm looking for the extreme points of the convex set $S\subset [-1,1]^{n\times 3}$ with $r\in S$ such that \begin{equation} r_{i} \ge r_{k} \iff i\ge k, \end{equation} where the first inequality ...
0
votes
0answers
217 views

computation complexity of OLS in estimating a VAR model

Could someone tell me the computation cost of using Ordinary least squares in estimating a Vector autoregression model? I am thinking the cost is O(n) where n is the number of the training instance. ...
3
votes
0answers
749 views

Hamiltonian Matrix Size in Schrodinger Equation

I'm attempting to solve the particle-in-a-box problem using Scipy (with the help of http://www.physics.buffalo.edu/phy410-505/2011/topic4/app2/index.html). At first, I used a 16x16 matrix to model the ...
12
votes
1answer
1k views

How exactly does the *full* multigrid algorithm run?

So I understand (or at least I believe I do) how a V-cycle runs. I've written in Matlab the 1-D, recursive version of a V-cycle. However, when I ran my code for FMG, my solution wasn't converging. I ...
7
votes
2answers
2k views

Shape regularity in higher dimensions

In Finite Element theory, and other methods in scientific computing for PDEs, one uses meshes which fulfill several regularity criteria, many of them being equivalent. It is of interest to have ...
3
votes
1answer
354 views

Limitations of Domain Decomposition Method (DDM) in Finite Element Analysis (FEA)?

The use of DDM in FEA makes parallel solution of the whole analysis e.g. assembly, solver etc possible. DDM splits the model in domains and runs them in parallel. Since there are interconnected nodes ...
4
votes
1answer
232 views

How do I solve an ODE Two-Point Boundary Value Problem?

I have a feeling my question is a very basic one, but I am not at all well versed in computational sciences. My equations are of the form: $$ y \in \mathbb{R}^3 \\ \dot{y}(t) = f(y(t)) \\ y_1(0) = a ...
4
votes
2answers
404 views

Effects of memory speed/architecture on Pardiso scaling

I am using a program that utilizes the PARDISO solver as part of the Intel math kernel library. I am currently in the process of deciding on a new computer to run the simulations on. I have a ...
1
vote
0answers
28 views

PCA performed on a configuration with scaled axes

Suppose a configuration $X\in\mathbb{R}^{n\times 2}$ is output of PCA on some high-dimensional data $Y\in\mathbb{R}^{n\times h}$. Note that this PCA is performed by $$X=Y\cdot U,$$ where columns of $U$...
8
votes
1answer
528 views

Nonlinear wave equation - Finite element or finite difference

I would like to know the which is more advantageous when it comes to solving nonlinear hyperbolic equations, Finite Element or Finite difference methods? Which method will be better in capturing ...
5
votes
2answers
187 views

Is computational science recommended as part of the typical undergraduate curriculum every computer science department should teach?

Computational science remains uncommon in many computer science departments, particularly in universities without an engineering school. Is it not considered part of the standard computer science ...
2
votes
1answer
84 views

Optimality criterion of PCA via recovered distances

It is stated in http://users.eecs.northwestern.edu/~yingwu/teaching/EECS510/Reading/Williams_NIPS01.pdf that the PCA mapping from $h$-dimensional data to low $k$-dimensional space minimizes $$\sum_{...
6
votes
3answers
814 views

What is the best way to get erfi with scipy?

I want this: http://mathworld.wolfram.com/Erfi.html But apparently scipy does not have this in its extensive special functions library. http://docs.scipy.org/doc/scipy/reference/special.html It is ...
3
votes
1answer
154 views

Approximation of a linear function with polynomials of degree 1

If I have the following problem $$-\mu u'' + u' = 1$$ with boundary conditions $u(0) = u'(1) = 1$ in the interval $\Omega = (0,1)$. The exact solution is $$u(x) = x + 1$$ Will the FEM approximation ...
6
votes
1answer
815 views

Nonlinear dynamics: algorithm suggest

I've just started a thesis on nonlinear dynamics which entails numerical analysis of the Duffing oscillator (DO). It's basically just a second order ODE, or equivalently a set of ODEs. Say, after ...
7
votes
1answer
3k views

Schur's Complement and Inverse of Block Matrices

Assume that we are given a block matrix of the form: $$ M = \left[ \begin{array}{cc} A & b \\ b^T & c \\ \end{array} \right] $$ where $b$ is a column vector. and $c$ is a scalar. Schur's ...
10
votes
1answer
2k views

Solving a simple Ax=b system in parallel with PETSc

I am new to the PETSc package. I have a ~4000x4000 matrix A in matrix-market format and I want to get PETSc to solve this using multiple processors. I know how to solve the system on a single ...
3
votes
2answers
590 views

Unimodular Matrix calculation

I know for a given matrix $M$, there exists a matrix $U$ over the integers with determinant $+1$ or $-1$ such that $UM=E$. I know $E$, but $M$ is not a square matrix. Is there any easy way to get $...
15
votes
1answer
617 views

What is the current state of polynomial preconditioners?

I wonder what has happened to polynomial preconditioners. I am interested in them, because they appear to be comparatively elegant from a mathematical perspective, but as far as I have read in surveys ...

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